3D mesh models are usually composed of triangles, each of which are represented by associated position, colour and normal components. The position is given by floating-point coordinates of its three corners, or vertices. Each vertex has a normal component associated, which is also a floating-point value. The normal component gives the spatial vertex orientation. In compressing such 3D mesh models, each of the position, colour and normal components are separately compressed. [D95]1 describes such compression. In [D95], a normal sphere, on which the end points of unit normals lie, is divided into eight octants and each octant consists of six sextants. Further subdividing a sextant, normals are referenced by the mean of the normal on the 1/48 sphere. However, the approach given in [D95] is only suitable when the model normals are spherically uniform distributed. Based on the observation that normals of 3D mesh models are usually not evenly distributed, [DYH02]2 proposes k-means clustering of normals for improved compression. However, in this approach the number of clusters k is fixed. Moreover, it always a hard task to decide k beforehand. Further, advantages available in [D95], such as the normal encoding parameterization, are not available any more in [DYK02].
Complex 3D mesh models are composed of several components, which are called connected components. These are defined in SBM013 as follows. Two polygons are neighbouring polygons if they share an edge. There exists a path between polygons pi and pj if there is a sequence of neighbouring polygons. A subset Oc of the mesh model O is called a connected component if there exists a path between any two polygons in Oc. Such mesh model is called a multi-connected model. Further, for multi-connected models, an effective compression scheme may discover the repeating features and then compress the transformation data. The orientations are one of the important parts of transformations data.